He was looking forward to the arrival of the messiah and for the dead to be resurrected in bodies shining brightly, and so naturally concluded that this was Jesus, the messiah, resurrected!
Paul did not think Jesus was God or was a part of the trinity. That is not what the messiah was. To Paul, Jesus was the king of the Jews (thus Paul consistently called Jesus "lord"), and his resurrection indicating the Messianic age was finally on its way. Jesus was but the first of a general resurrection event that Paul was confident would occur in his life time. Paul referred to Jesus as the "first fruits" because he saw Jesus as the prototype for the resurrection, a man set apart to be the first, not a part of the trinity.
Romans 8:29 For those God foreknew he also predestined to be conformed to the image of his Son, that he might be the firstborn among many brothers and sisters.
1 Corinthians 6:14 By his power God raised the Lord from the dead, and he will raise us also.
1 Corinthians 15:20 But Christ has indeed been raised from the dead, the firstfruits of those who have fallen asleep.These verses in Acts make clear that Paul believed Jesus was appointed the messiah, not born the messiah.
Acts 17:30 Therefore having overlooked the times of ignorance, God is now declaring to men that all people everywhere should repent, 31 because He has fixed a day in which He will judge [u]the world in righteousness [v]through a Man whom He has appointed, having furnished proof to all men [w]by raising Him from the dead.”Paul decided his message was for gentiles as well as Jews. This is rather odd, given he was a Pharisee and given Jesus' message was for the Jews, and Paul was met with some resistance from the apostles, who thought a gentile follower of Jesus should become a Jew - to them (and Paul) Jesus was giving a new perspective on the Jewish religion, not starting a new one. However, as Paul said:
Romans 3:29 Or is God the God of Jews only? Is he not the God of Gentiles too? Yes, of Gentiles too, 30 since there is only one God, who will justify the circumcised by faith and the uncircumcised through that same faith.Romans 11 indicates Paul thought Israel would be saved, and that he hoped his mission to the gentiles would be a part of that process.
Paul expected the resurrection very soon.
Romans 13:11 And do this, understanding the present time: The hour has already come for you to wake up from your slumber, because our salvation is nearer now than when we first believed. 12 The night is nearly over; the day is almost here. So let us put aside the deeds of darkness and put on the armor of light.
1 Corinthians 7:29 What I mean, brothers and sisters, is that the time is short. ... 31 those who use the things of the world, as if not engrossed in them. For this world in its present form is passing away.
1 Thessalonians 4:13 Brothers and sisters, we do not want you to be uninformed about those who sleep in death, so that you do not grieve like the rest of mankind, who have no hope. 14 For we believe that Jesus died and rose again, and so we believe that God will bring with Jesus those who have fallen asleep in him. 15 According to the Lord’s word, we tell you that we who are still alive, who are left until the coming of the Lord, will certainly not precede those who have fallen asleep. 16 For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. 17 After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever.
Paul expected the righteous to be resurrection in new bodies that shine as bright as stars, just as foretold in Daniel and just as he had seen for Jesus:
1 Corinthians 15:5 But someone will ask, “How are the dead raised? With what kind of body will they come?” ... 40 There are also heavenly bodies and there are earthly bodies; but the splendor of the heavenly bodies is one kind, and the splendor of the earthly bodies is another. 41 The sun has one kind of splendor, the moon another and the stars another; and star differs from star in splendor.
42 So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; 43 it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; 44 it is sown a natural body, it is raised a spiritual body.
2 Corinthians 5:1 For we know that if the earthly tent we live in is destroyed, we have a building from God, an eternal house in heaven, not built by human hands. 2 Meanwhile we groan, longing to be clothed instead with our heavenly dwelling, 3 because when we are clothed, we will not be found naked. 4 For while we are in this tent, we groan and are burdened, because we do not wish to be unclothed but to be clothed instead with our heavenly dwelling, so that what is mortal may be swallowed up by life. 5 Now the one who has fashioned us for this very purpose is God, who has given us the Spirit as a deposit, guaranteeing what is to come.
More on Paul's beliefs here.